1. The Sun The Sun’s Spectrum
Earlier in the course, I told you stellar spectra are black bodies
Why are there all these features?

2. + Spectral Lines High resolution solar spectrum
In dense inner part, light gets randomized – black body spectrum
Light passes through cooler stellar atmosphere
But some wavelengths get absorbed! + -

3. Stellar spectra
Approximate black body spectrum – color tells you temperature
Red is cool, blue is hot
Spectral lines tell you a lot about the star
Different lines for each element (and ionization state)
Strength tells you about composition and temperature

4. Composition of a Typical Star (Sun)
73.46% Hydrogen
24.85% Helium
0.77% Oxygen
0.29% Carbon
0.16% Iron
0.12% Neon
0.09% Nitrogen
0.07% Silicon
0.05% Magnesium
~0.14% Other

5. The Photosphere
The point at which gas is thick enough that we can’t see through it
This is a little shallower towards the edge
Limb darkening
Here we see shallow and cool
Here we see deep and hot

6. The Stefan-Boltzmann Law
Earlier, we discussed the energy density for black body radiation
Imagine a region filled with black body radiation with a hole where it can flow out
Only half of it is moving at all outwards
This half is moving out at average speed ½c
The flux* (power/area) for this flow is:
Define the Stefan-Boltzmann constant 
Then the flux is given by
*Confusingly, called R in the book

7. Total Luminosity of a Star
If the surface temperature of the star is T, we can multiply by the surface area of the star to get the total luminosity L
For example, we can use this to get the surface temperature of the Sun:
Solve for the surface temperature
Another way to write the luminosity formula
Divide by the same expression for the Sun

8. What Powers the Sun? The Sun has been shining for > 4 billion years
Could it be chemical energy?
The energy per kg is:
Not nearly enough
Could it be gravitational potential energy?
Perhaps nuclear power?
Looks likely!

9. The Proton-Proton Chain, Step 1
The Sun is made primarily of hydrogen
Which has the most energy per nucleon
Hydrogen must combine to make some heavier nucleus
Simplest process: 1H + 1H  2He
The problem:
2He is very unstable, and this process immediately reverses itself
To stabilize it, the 2He must immediately + decay to make 2H
The effective interaction (so far) is p+ p+ p+ n0 p+  e+
1H + 1H  2H + e+ + e

10. Energy from Fusion Reactions
For simple fusion reactions, where protons and neutrons are rearranged, easy to find the energy produced
Consider a process like:
From previous arguments, the energy produced would be
But the charge of the nuclei is conserved, so
For other processes, like + decay, we can use previously found formulas
A + B  C + 

11. Sample Problem
Find the energy for each substep in the process 1H + 1H  2H + e+ + e
The two steps are
The first step is a simple fusion
The second step is a standard + decay
Total energy for this process is
1H + 1H 2He
2He  2H + e+ + e

12. Why the Proton-Proton chain is slow+ p+ n0 p+ + +
1H + 1H  2H + e+ + e MeV  e+
The protons repel each other until they get close together
They therefore must be moving at high speed to get even a little close
They then need to quantum tunnel the rest of the way
This has a very low probability
To get it to work, it then needs to immediately + decay
To overcome all these difficulties, the temperature must be very hot
Minimum about 10 million K
In the Sun, the central temperature is about 15 million K
The process is very temperature sensitive
Even a small change in temperature causes a very large change in rate

13. The Proton-Proton Chain, Steps 2 – 4+ p+ + + p+ p+
1H + 1H  2H + e+ + e MeV  e+ n0
The next few steps go much faster
Step 2: The positron immediately finds an electron to annihilate with
Step 3: The 2H nucleus finds another proton to combine with to make 3He
Step 4: Two 3He nuclei find each other and make 4He plus two protons e+  e- +
e+ + e–   +  MeV p+ n0 + 
2H + 1H  3He +  MeV n0 + p+
2 3He  4He + 2 1H MeV

14. The Proton-Proton Chain, Overview
The net reaction is:
The neutrinos leave and carry 2% of this energy
The photons that were produced, and the kinetic energy of other products, heat the center of the Sun
The 98% now works its way to the surface of the Sun
4 1H + 2 e–  4He + 2  MeV

15. Detecting the Neutrinos
Neutrinos have a very low cross-section to interact with anything
But there are an enormous number of them streaming towards the Earth
Neutrino detectors detect a very small fraction of these neutrinos
Homestake neutrino detector
Sudbury Neutrino Observatory

16. The Sun imaged in neutrinos
Neutrino Detectors
The Sun imaged in neutrinos
Super Kamiokande

17. Ways to Move Heat Three ways that heat can move:
Conduction – heat by physical contact
Too slow in stars
Convection – the flow of fluids
Important in the Sun and other stars
Radiation – the flow of electromagnetic radiation

18. How Heat Moves in the Sun
There are three regions in the interior of the Sun
The core
Where the energy is generated
The radiative zone
Heat moves by radiation
Note this is largest region
The convective zone
Heat moves by convection